Covariance Recovery and CRB Analysis for DOA Estimation by Mixed One-Bit Quantized Signals

Direction-of-Arrival (DOA) estimation is a fundamental task in array signal processing. Although one-bit quantization significantly reduces hardware complexity and cost, it introduces substantial quantization error that impairs estimation accuracy. To mitigate this, we propose a mixed one-bit quantization method that integrates one-bit and full-resolution sensors. We derive a theoretical expression that relates the mixed one-bit quantized observations to the pre-quantization covariance matrix, enabling reliable reconstruction for subsequent DOA estimation. Furthermore, we formulate the corresponding Cramér-Rao Bound (CRB) to characterize the theoretical performance of the proposed method. Experiment results show that our method consistently outperforms one-bit quantization in DOA estimation tasks and effectively preserves signal features, thereby enhancing downstream processing capabilities such as target recognition.